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arXiv · 2009.14382

Algebraic Degree Periodicity in Recurrence Sequences

Daqing Wan·Hang Yin
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Abstract

The degree sequence of the algebraic numbers in an algebraic linear recurrence sequence is shown to be virtually periodic. This is proved using the Skolem-Mahler-Lech theorem. It has applications to the degree sequence and the minimal polynomial sequence for exponential sums over finite fields. The degree periodicity also holds for some more complicated non-linear recurrence sequences. We give one example from the iterations of a polynomial map. This depending on the dynamic Mordell-Lang conjecture which has been proved in some cases.

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Daqing Wan, Hang Yin. 2020-09-30. Algebraic Degree Periodicity in Recurrence Sequences. https://arxiv.org/abs/2009.14382

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